Problem: Simplify the following expression: $\sqrt{175} - \sqrt{112}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{175} - \sqrt{112}$ $= \sqrt{25 \cdot 7} - \sqrt{16 \cdot 7}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{7} - \sqrt{16} \cdot \sqrt{7}$ $= 5\sqrt{7} - 4\sqrt{7}$ Finally, simplify by combining the terms. $= ( 5 - 4 )\sqrt{7} = \sqrt{7}$